1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 02db0f525a288673aba4923c6b88677071850d51.

2 Data

Case data is captured from the NICD National COVID-19 Daily Report [3]. This contains the daily cases reported by the NICD for South Africa by province. Data is shown by specimen reported date. Most recent data is excluded due to incomplete reporting of tests in last number of days.

The following fixes are applied:

  1. Calculate daily new cases from cumulative data captured.
  2. Add a total for South Africa as a whole.
  3. Add records (with 0 case count) in periods where no cases were recorded.
  4. Recalculate cumulative figures.
  5. Data captured for speciments reported in the 3 days before the reporting date is excluded due as cases reporting is likely incomplete. In future versions of this report this may be changed.

3 Methodology

The methodology is described in detail here.

4 Results

4.1 Cases

Below a 7-day moving average daily case count is plotted by province on a log scale since start of the epidemic:

Below the above chart is repeated for the last 30-days:

4.2 Current \(R_{t,m}\) estimates by Province

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Province
province Count (Week) Week Ending Reproduction Number [95% Confidence Interval]
Eastern Cape 119 2021-03-24 0.9 [0.76 - 1.08]
Free State 772 2021-03-24 1.0 [0.95 - 1.10]
Gauteng 1,942 2021-03-24 0.9 [0.90 - 0.99]
KwaZulu-Natal 679 2021-03-24 0.7 [0.64 - 0.76]
Limpopo 178 2021-03-24 0.9 [0.78 - 1.06]
Mpumalanga 784 2021-03-24 0.9 [0.84 - 0.97]
North West 637 2021-03-24 0.9 [0.86 - 1.01]
Northern Cape 615 2021-03-24 0.9 [0.83 - 0.98]
Western Cape 935 2021-03-24 1.0 [0.94 - 1.07]
South Africa 6,661 2021-03-24 0.9 [0.89 - 0.94]
Estimated Effective Reproduction Number by Province

Estimated Effective Reproduction Number by Province

4.3 Maps of Effective Reproduction Number

Below estimates of the reproductive number is plotted on maps of South Africa [4].

Estimated Effective Reproduction Number Based on Cases by Province

Estimated Effective Reproduction Number Based on Cases by Province

4.4 Estimated Effective Reproduction Number for South Africa over Time

Below the results for South Africa ove the last 90 days is plotted.

Estimated Effective Reproduction Number Based on Cases for South Africa over Time

Estimated Effective Reproduction Number Based on Cases for South Africa over Time

4.5 Map of Effective Reproduction Number Over Last 60 Days

Below the reproduction number by week by province is animated:

4.6 Estimated Effective Reproduction Number for Provinces over Time

The results for each province over last 90 days is plotted below.

4.6.1 Eastern Cape

Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time

Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time

4.6.2 Free State

Estimated Effective Reproduction Number Based on Cases for Free State over Time

Estimated Effective Reproduction Number Based on Cases for Free State over Time

4.6.3 Gauteng

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

4.6.4 KwaZulu-Natal

Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time

Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time

4.6.5 Limpopo

Estimated Effective Reproduction Number Based on Cases for Limpopo over Time

Estimated Effective Reproduction Number Based on Cases for Limpopo over Time

4.6.6 Mpumalanga

Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time

Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time

4.6.7 Northern Cape

Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time

Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time

4.6.8 North West

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

4.6.9 Western Cape

Estimated Effective Reproduction Number Based on Cases for Western Cape over Time

Estimated Effective Reproduction Number Based on Cases for Western Cape over Time

4.7 Detailed Results

Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.

5 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection.
  • It’s sensitive to changes in case detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred earlier. These figures have not been shifted back.

Despite these limitation it is believed that the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

Having said all the above it would appear that the effective reproduction number was reasonably high in South Africa from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.

6 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133.

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013.

[3] National Institute for Communicable Diseases, “National COVID-19 Daily Report,” 2021.

[4] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018.